V. L. Girko

An Introduction to Statistical Analysis of Random Arrays (eBook, PDF)

• Format: PDF

Produktbeschreibung

Frontmatter -- CONTENTS -- List of basic notations and assumptions -- Preface and some historical remarks -- Chapter 1. Introduction to the theory of sample matrices of fixed dimension -- Chapter 2. Canonical equations -- Chapter 3. The First Law for the eigenvalues and eigenvectors of random symmetric matrices -- Chapter 4. The Second Law for the singular values and eigenvectors of random matrices. Inequalities for the spectral radius of large random matrices -- Chapter 5. The Third Law for the eigenvalues and eigenvectors of empirical covariance matrices -- Chapter 6. The first proof of the Strong Circular Law -- Chapter 7. Strong Law for normalized spectral functions of nonselfadjoint random matrices with independent row vectors and simple rigorous proof of the Strong Circular Law -- Chapter 8. Rigorous proof of the Strong Elliptic Law -- Chapter 9. The Circular and Uniform Laws for eigenvalues of random nonsymmetric complex matrices with independent entries -- Chapter 10. Strong V-Law for eigenvalues of nonsymmetric random matrices -- Chapter 11. Convergence rate of the expected spectral functions of symmetric random matrices is equal to 0(n-1/2) -- Chapter 12. Convergence rate of expected spectral functions of the sample covariance matrix ?m¿(n) is equal to 0(n-1/2) under the condition m¿n-1?c<1 -- Chapter 13. The First Spacing Law for random symmetric matrices -- Chapter 14. Ten years of General Statistical Analysis (The main G-estimators of General Statistical Analysis) -- References -- Index

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Produktdetails

• Verlag: De Gruyter
• Seitenzahl: 699
• Erscheinungstermin: 5. November 2018
• Englisch
• ISBN-13: 9783110916683
• Artikelnr.: 56304600

Inhaltsangabe

Frontmatter -- CONTENTS -- List of basic notations and assumptions -- Preface and some historical remarks -- Chapter 1. Introduction to the theory of sample matrices of fixed dimension -- Chapter 2. Canonical equations -- Chapter 3. The First Law for the eigenvalues and eigenvectors of random symmetric matrices -- Chapter 4. The Second Law for the singular values and eigenvectors of random matrices. Inequalities for the spectral radius of large random matrices -- Chapter 5. The Third Law for the eigenvalues and eigenvectors of empirical covariance matrices -- Chapter 6. The first proof of the Strong Circular Law -- Chapter 7. Strong Law for normalized spectral functions of nonselfadjoint random matrices with independent row vectors and simple rigorous proof of the Strong Circular Law -- Chapter 8. Rigorous proof of the Strong Elliptic Law -- Chapter 9. The Circular and Uniform Laws for eigenvalues of random nonsymmetric complex matrices with independent entries -- Chapter 10. Strong V-Law for eigenvalues of nonsymmetric random matrices -- Chapter 11. Convergence rate of the expected spectral functions of symmetric random matrices is equal to 0(n-1/2) -- Chapter 12. Convergence rate of expected spectral functions of the sample covariance matrix ?m"(n) is equal to 0(n-1/2) under the condition m"n-1?c<1 -- Chapter 13. The First Spacing Law for random symmetric matrices -- Chapter 14. Ten years of General Statistical Analysis (The main G-estimators of General Statistical Analysis) -- References -- Index